where \(f(n)\)  is the running time of a unique decoding algorithm for \(\mathcal {C}\) .
Otherwise, we return \(\mathcal {L}(\tilde{y},\mathcal {C},\mathcal {C}^{\prime })=\emptyset \)  with the same running time
of the preceding case
 In the case \(\tilde{y}\)  is not \((1/2-\sqrt{\eta })\) -close to \(\mathcal {C}^{\prime }\) , but the SOS program turns out to be feasible, some of the calls to the unique decoding algorithm of \(\mathcal {C}\)  (issued by the list decoding framework) might be outside all unique decoding balls. Such cases may be handled by returning failure if the algorithm does not terminate by the time \(f(n)\) . Even if a codeword in \(\mathcal {C}\)  is found, the pruning step of list decoding [1]} will return an empty list for \(\mathcal {L}(\tilde{y},\mathcal {C},\mathcal {C}^{\prime })\)  since \(\tilde{y}\)  is not \((1/2-\sqrt{\eta })\) -close to \(\mathcal {C}\) ..

